{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "9e10ba36",
   "metadata": {},
   "source": [
    "# Lagrange Interpolation\n",
    "## Mathmatical background\n",
    "suppose function goes through n known points $(x_0,y_0),(x_1,y_1),(x_2,y_2),\\dots ,(x_n,y_n)$,then interpolation polynomial should be like:\n",
    "\n",
    "$$\n",
    "    L_n(x) = \\displaystyle\\sum_{k=0}^{n}{y_kl_k(x)}\n",
    "$$\n",
    "\n",
    "where $l_k(x)$ stands for interpolation base function:\n",
    "\n",
    "$$\n",
    "    l_k(x) = \\frac{(x-x_0)(x-x_1)(x-x_2)\\cdots(x-x_{k-1})(x-x_{k+1})\\cdots(x-x_n)}{(x_k-x_0)(x_k-x_1)(x_k-x_2)\\cdots(x_k-x_{k-1})(x_k-x_{k+1})\\cdots(x_k-x_n)}\n",
    "$$\n",
    "\n",
    "we make this following convention:\n",
    "\n",
    "$$\n",
    "\\left\\{\n",
    "\\begin{array}{ll}\n",
    "\\omega_{n+1}(x) & = & (x-x_0)(x-x_1)(x-x_2)\\cdots(x-x_n)\\\\\n",
    "\\omega^{\\prime}_{n+1}(x_k) & = & (x_k-x_0)(x_k-x_1)(x_k-x_2)\\cdots(x_k-x_{k-1})(x_k-x_{k+1})\\cdots(x_k-x_n)\n",
    "\\end{array}\n",
    "\\right .\n",
    "$$\n",
    "\n",
    "then interpolation polynomial could be expressed as:\n",
    "\n",
    "$$\n",
    "    L_n(x) = \\displaystyle\\sum_{k=0}^{n}{y_k\\frac{\\omega_{n+1}(x)}{(x-x_k)\\omega^{\\prime}_{n+1}(x_k)}}\n",
    "$$\n",
    "\n",
    "as we use higher order polynomials to approximate possible original function, the remainder should be like:\n",
    "\n",
    "$$\n",
    "    R_n(x) = f(x) - L_n(x) = \\frac{f^{(n+1)}(\\xi)}{(n+1)!}\\omega_{n+1}(x) \n",
    "$$\n",
    "\n",
    "where $\\xi \\in (a,b)$ and dependent on $x$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3c30f83c",
   "metadata": {},
   "source": [
    "## Notice\n",
    "1. for each new known points adding to polynomial model, each base function should be recalculated, which is time-comsuming. In other words, calcualtion result could not be reused.\n",
    "2. as is shown in interpolation polynomials, the order of polynomial depends on number of known points. Yet notice that Kunge Phenomenon still exists.\n",
    "\n",
    "## More\n",
    "If we expand lagrange interpolation polynomial, we will get the same form of <font color=vermillion><b>Vandermonde determinant</font></b>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2f3ce8e8",
   "metadata": {},
   "source": [
    "# Newton Interpolation\n",
    "## Mathmatical background\n",
    "to begin with, we define polynomial as following:\n",
    "\n",
    "$$\n",
    "    P_n(x) = a_0 + a_1(x-x_0) + a_2(x-x_0)(x-x_1) +\\cdots + a_n(x-x_0)(x-x_1)\\cdots(x-x_n)\n",
    "$$\n",
    "\n",
    "then our goal is to find coefficent ${a_0, a_1, a_2 ,\\cdots, a_n}$, these coeffcients could also be called <font color=sapphire><b>difference quotient</b></font>;<br>\n",
    "higher order difference quotient could be derived by the lower order by using recursion formula<br> \n",
    "first order:\n",
    "\n",
    "$$\n",
    "    f[x_i, x_j] = \\frac{f(x_i)-f(x_j)}{x_i-x_j}\n",
    "$$\n",
    "\n",
    "second order:\n",
    "\n",
    "$$\n",
    "    f[x_i, x_j, x_k] = \\frac{f[x_i, x_j]-f[x_j, x_k]}{x_i-x_k}\n",
    "$$\n",
    "\n",
    "then, we could find k-order:\n",
    "\n",
    "$$\n",
    "    f[x_0, x_1, \\cdots, x_k] = \\frac{f[x_0, x_1,\\cdots,x_{k-2},x_k]-f[x_0, x_1, \\cdots, x_{k-1}]}{x_k-x_{k-1}}\n",
    "$$\n",
    "\n",
    "and the other one is also true:\n",
    "\n",
    "$$\n",
    "    f[x_0, x_1, \\cdots, x_k] = \\frac{f[x_1, x_2,\\cdots,x_k]-f[x_0, x_1, \\cdots, x_{k-1}]}{x_k-x_{0}}\n",
    "$$\n",
    "\n",
    "one important property of difference quotient is:\n",
    "\n",
    "$$\n",
    "    f[x_0, x_1, \\cdots, x_k] = \\displaystyle\\sum_{j=0}^{k}{\\frac{f(x_j)}{(x_j-x_0)\\cdots(x_j-x_{j-1})(x_j-x_{j+1})\\cdots(x_j-x_k)}}\n",
    "$$\n",
    "\n",
    "and difference quotient is also associate with gradient:\n",
    "\n",
    "$$\n",
    "    f[x_0, x_1, \\cdots, x_k] = \\frac{f^{(n)}(\\xi)}{n!} , \\xi \\in (a,b)\n",
    "$$\n",
    "\n",
    "## Notice\n",
    "1. newton interpolation is faster than lagrange interpolation in that new points will not cause the re-calculation of the whole model\n",
    "2. yet, difference quotient is not that easy to calculate"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "21316fe0",
   "metadata": {},
   "source": [
    "# Hermite Interpolation\n",
    "## Mathmatical background\n",
    "1. to begin with, we not only wants data close enough to function, but the first order derivation as well.<br>\n",
    "then, by using undeterminated coefficient method, we could easily calculate coefficient of each polynomial terms."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "14348c14",
   "metadata": {},
   "source": [
    "# Piecewise Interpolation\n",
    "1. to avoid Krunge Phenomenon, we could split interval into several sub-intervals, and apply Lagrange or Hermite interpolation in each sub-intervals, this could garantee the closeness in value, yet we could not garantee the smoothness of the connction points, which is the interval splitting point."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "95de6ecb",
   "metadata": {},
   "source": [
    "# Spline Interpolation\n",
    "1. most commonly used interpolation method, in this case, we assume <font color=vermillion><b>first order and second order derivatives</b></font> are the same for both interpolation polynomials and original function.\n",
    "2. in this case, we could construct interpolation base function and delegate its order. The most commonly used order is 3, which is also called <font color=vermillion><b>cubic spline interpolation</b></font>\n",
    "\n",
    "<hr>\n",
    "\n",
    "1. to start with, as we are going to apply cubic polynomial, we need to specify 4 coefficient, in n intervals, total restriction function should be $4n$. we assume the polynomial function is:\n",
    "\n",
    "$$\n",
    "    S(x) = \\displaystyle\\sum_{j=0}^{n}{[y_j\\alpha(x)+m_j\\beta(x)]}\n",
    "$$\n",
    "\n",
    "where $y_j = S(x)$ and $m_j = S^{\\prime}(x)$, both two are constants<br>\n",
    "in this case, we just apply hermite polynomial form to spline polynomial. Base function is\n",
    "\n",
    "$$\n",
    "\\alpha_j(x) = \n",
    "\\left\\{\n",
    "\\begin{array}{ll}\n",
    "{(\\frac{x-x_{j-1}}{x_j-x_{j-1}}})^2(1+2\\frac{x-x_j}{x_{j-1}-x_j}) &, x_{j-1} \\le x \\le x_j \\\\\n",
    "{(\\frac{x-x_{j+1}}{x_j-x_{j+1}}})^2(1+2\\frac{x-x_j}{x_{j+1}-x_j}) &, x_{j} \\le x \\le x_{j+1} \\\\\n",
    "0 &, elsewhere\n",
    "\\end{array}\n",
    "\\right .\n",
    "$$\n",
    "\n",
    "$$\n",
    "\\beta_j(x) = \n",
    "\\left\\{\n",
    "\\begin{array}{ll}\n",
    "{(\\frac{x-x_{j-1}}{x_j-x_{j-1}}})^2({x-x_j}) &, x_{j-1} \\le x \\le x_j \\\\\n",
    "{(\\frac{x-x_{j+1}}{x_j-x_{j+1}}})^2({x-x_j}) &, x_{j} \\le x \\le x_{j+1} \\\\\n",
    "0 &, elsewhere\n",
    "\\end{array}\n",
    "\\right .\n",
    "$$\n",
    "\n",
    "2. then, this following conidition will provide $(n+1)$ restriction\n",
    "\n",
    "$$\n",
    "    S(x_j) = y_j\n",
    "$$\n",
    "\n",
    "3. next we devide target interval $(a,b)$ into n continuous sub-interval $(a,x_0),(x_0,x_1),\\cdots,(x_j,x_{j+1},\\cdots,(x_n,b))$, with condition $x_{j}, x_{j+1} \\in (a,b)$\n",
    "4. then, in each interval, we apply piecewise interpolation, and only take two points to construct out hermite interpolation polynomial. Due to the fact that first order and second order derivitives should be continuous, we could then have $3(n-1)$ restriction function\n",
    "\n",
    "$$\n",
    "\\left\\{\n",
    "\\begin{array}{ll}\n",
    "S(x_j - 0) & = & S(x_j +0) \\\\\n",
    "S^{\\prime}(x_j - 0) & = & S^{\\prime}(x_j +0) \\\\\n",
    "S^{\\prime\\prime}(x_j - 0) & = & S^{\\prime\\prime}(x_j +0) \\\\\n",
    "\\end{array}\n",
    "\\right .\n",
    "$$\n",
    "\n",
    "5. now we have $(n+1)+3(n-1) = 4n-2$ restriction function, the lsat 2 we could use boudary condtion:\n",
    "\n",
    "$$\n",
    "\\left\\{\n",
    "\\begin{array}{ll}\n",
    "S^{\\prime}(x_0) & = &  f_0^{\\prime}(x)\\\\\n",
    "S^{\\prime}(x_n) & = &  f_n^{\\prime}(x)\\\\\n",
    "\\end{array}\n",
    "\\right .\n",
    "$$\n",
    "$$\n",
    "\\left\\{\n",
    "\\begin{array}{ll}\n",
    "S^{\\prime\\prime}(x_0) & = &  f_0^{\\prime\\prime}(x)\\\\\n",
    "S^{\\prime\\prime}(x_n) & = &  f_n^{\\prime\\prime}(x)\\\\\n",
    "\\end{array}\n",
    "\\right .\n",
    "$$\n",
    " \n",
    "6. in this case, $\\alpha_j(x)$, $\\beta_j(x)$ and $y_j$ are known function or constant, here we need to deduct $m_j$, then we could get the close form of $S(x)$ "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "721e2d10",
   "metadata": {},
   "source": [
    "# scipy interpolation packages\n",
    "1. scipy.interpolate package\n",
    "2. most basic univariate interpolation method: interp1d, this will use <font color=vermillion>s<b>pline interpolation</b></font> \n",
    "<hr>\n",
    "note that most interpolation functions takes x and corresponding y as input and generate one callable function, then we could use this function to calculate interpolated y."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4fafd00c",
   "metadata": {},
   "source": [
    "$$\n",
    "    f(x) = sin(x^2 + e^x) + tan(x^2)\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5c275272",
   "metadata": {},
   "source": [
    "## 1d interpolation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "82da7a62",
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.interpolate import interp1d\n",
    "import numpy as np\n",
    "import matplotlib\n",
    "from matplotlib import pyplot as plt\n",
    "\n",
    "x_range = np.arange(0,10,0.5)\n",
    "y_ori = np.sin(np.power(x_range,2) + np.exp(x_range)) + np.tan(np.power(x_range,2))\n",
    "\n",
    "interp_model = interp1d(x_range,y_ori)\n",
    "x_out = np.linspace(0.1,9,1000)\n",
    "y_int = interp_model(x_out)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "1600b774",
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "fig, ax = plt.subplots(1,1,figsize=(5,5),\n",
    "                      facecolor=\"whitesmoke\",\n",
    "                      edgecolor='gray')\n",
    "ax.scatter(x_range, y_ori, lw=.3, marker='>', color=\"orange\", label='origin data')\n",
    "#ax.scatter(x_out, y_int, lw=.1, marker=\"x\", color='green',label=\"interpolation data\")\n",
    "ax.plot(x_out, y_int, lw=.5, ls='-', color='blue',label=\"interpolation\")\n",
    "ax.legend(loc='best')\n",
    "ax.grid(alpha=0.4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "a8a9fd8c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "kinds = [\"nearest\", \"zero\",\"slinear\",\"quadratic\",\"cubic\"]\n",
    "colors = [\"magenta\", \"green\", \"purple\", \"blue\", \"black\"]\n",
    "labels = [\"nearest\", \"zero\",\"slinear\",\"quadratic\",\"cubic\"]\n",
    "\n",
    "fig, ax = plt.subplots(1,1,figsize=(5,5),\n",
    "                      facecolor=\"whitesmoke\",\n",
    "                      edgecolor='gray')\n",
    "ax.scatter(x_range, y_ori, lw=.3, marker='>', color=\"orange\", label='origin data')\n",
    "\n",
    "for kind,color,label in zip(kinds,colors,labels):\n",
    "    f = interp1d(x_range, y_ori, kind=kind)\n",
    "    y_interp = f(x_out)\n",
    "    ax.plot(x_out, y_interp, lw=.5, ls='-', color=color,label=label)\n",
    "\n",
    "ax.legend(loc='best')\n",
    "ax.grid(alpha=0.4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d5176409",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.11.7"
  },
  "toc": {
   "base_numbering": 1,
   "nav_menu": {},
   "number_sections": true,
   "sideBar": true,
   "skip_h1_title": false,
   "title_cell": "Table of Contents",
   "title_sidebar": "Contents",
   "toc_cell": false,
   "toc_position": {},
   "toc_section_display": true,
   "toc_window_display": true
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
